SuDoku

1. Object Oriented Programming 31695 Final Course Project SuDoku

2. Files Organization • Download sudoku.zip from:http://www.samyzaf.com/braude/OOP/PROJECTS/sudoku.zip • Unzip this file in drive C (or D), so your project willreside in: C:\sudoku (or D:\sudoku) • You will find there all the files you need for the project • You can also access individual files from:http://www.samyzaf.com/braude/OOP/PROJECTS/Sudoku • Make sure to edit the README.txt file and enter allthe required information (name, email, phones, etc.) • After completing your project, you should zip thisdirectory back to sudoku.zip and upload it to:http://www.samyzaf.com/braude/OOP/upload.html

3. Submission Policy • Deadline: June 07, 2014 (till midnight) • Upload site will be closed after this date! • Work in pairs is OK (but not triples!) • A 30 minutes project review will be held for each partner separately! • Office slots for project reviews will be posted early June • Use the scheduling tool to schedule a meeting:http://www.samyzaf.com/cgi-bin/appsched.cgi

4. SuDoKu Puzzle Rules • Information based on Project Euler: http://projecteuler.net • The objective of a SuDoKu puzzle is to replace the blanks (or zeroes) in a 9x9 grid such that each row, column, and 3x3 box contains each of the digits 1 to 9 • The Diagonal-SuDoKu puzzle requires each diagonal contains all 1-9 digits • Below is a textual display of a typical puzzle grid and its solution grid: SUDOKU PUZZLE SOLUTION +-------+-------+-------+ +-------+-------+-------+ | 0 0 3 | 0 2 0 | 6 0 0 | | 4 8 3 | 9 2 1 | 6 5 7 | | 9 0 0 | 3 0 5 | 0 0 1 | | 9 6 7 | 3 4 5 | 8 2 1 | | 0 0 1 | 8 0 6 | 4 0 0 | | 2 5 1 | 8 7 6 | 4 9 3 | +-------+-------+-------- --------+-------+-------+ | 0 0 8 | 1 0 2 | 9 0 0 | | 5 4 8 | 1 3 2 | 9 7 6 | | 7 0 0 | 0 0 0 | 0 0 8 | | 7 2 9 | 5 6 4 | 1 3 8 | | 0 0 6 | 7 0 8 | 2 0 0 | | 1 3 6 | 7 9 8 | 2 4 5 | +-------+-------+-------- ----------------+-------+ | 0 0 2 | 6 0 9 | 5 0 0 | | 3 7 2 | 6 8 9 | 5 1 4 | | 8 0 0 | 2 0 3 | 0 0 9 | | 8 1 4 | 2 5 3 | 7 6 9 | | 0 0 5 | 0 1 0 | 3 0 0 | | 6 9 5 | 4 1 7 | 3 8 2 | +-------+-------+-------+ +-------+-------+-------+

5. SuDoKu – Graphical View • We will also be interested in drawing SuDoKu diagrams on top of a graphical canvas as shown here: SUDOKU PUZZLE SOLUTION

6. SuDoKu - Solution • A well constructed SuDoku puzzle has a unique solution and can be solved by logic, although it may be necessary to employ "guess and test" methods in order to eliminate options (there is much contested opinion over this). • The complexity of the search determines the difficulty of the puzzle • the example above is considered easy because it can be solved by straight forward direct deduction

7. http://www.mirror.co.uk/news/weird-news/worlds-hardest-sudoku-can-you-242294http://www.mirror.co.uk/news/weird-news/worlds-hardest-sudoku-can-you-242294

8. USA Today Journal, June 11 2006 Can your program solve this one?

9. Sudoku Puzzle Databases • The zip package you have downloaded contains several puzzle databases • easy10.txt • These are 10 very easy puzzles you should use for tests • Your program should handle these puzzles very quickly!(so you don’t have to wait to long for tests) • top160.txt • A set of 160 very difficult puzzles • top2500.txt • If you need more: database with 2500 puzzles • diag200.txt • 200 diagonal Sudoku puzzles

10. Your Mission • You need to • Build classes: Cell, Sudoku, Sudokiller, Partition • Define several function for reading puzzles from files, finding all the possible solutions of a Sudoku puzzle, and printing solutions in a pretty format (textual and graphical!) • Use the files: • cell.py • sudoku.py • sudokiller.py • file_solver.py • Make sure to follow the directions there precisely, and complete the missing code so that they eventually work

11. Graphics • The graphics that we use for drawing our Sudoku boards are:graphics.pypoint.pyline.pyrectangle.py • These files are contained in the sudoku.zip package, so you do not have to download them • These files implement our basic graphical environment. Specifically, it defines a canvas window on which we can draw points, lines, rectangles, and other geometrical shapes • There is no need to read or understand the code in these modules, you’re only required to use it for drawing your Sudoku puzzles • If you want to learn more about the Tkinter graphics programming, you may start with: http://www.tkdocs.com/tutorial/

12. Task 1: Cell Class class Cell(Rectangle): size = 30 font = "Consolas 12 bold" color = "Maroon" outline = "black" def __init__(self, data=0): Rectangle.__init__(self, 0, 0, self.size, self.size) self._data = data self.id = 0 # Canvas id def data(self, new_data=None): # Two uses: # 1. Change the Cell data to new_data: c.data(7) # 2. Return the current data: c.data() def draw(self): # Draw Cell object on the canvas # Graphics should consist of a Rectangle object and a text label # Label is: 1, 2, 3, ..., 9 # An empty cell (0) has no label # Key command: # canvas.create_text(p.x, p.y, text=label, font=self.font, fill=self.color) # p is the Cell center Point

13. Cell Class Test • If you have designed your Cell class well, then it should pass the following test defCell_test(): a = Cell(7) b = Cell(2) c = Cell(0) a.place(200,130) b.place(70,105) c.place(230,180) a.draw() b.draw() c.draw() print c.size show_canvas()

14. Task 2: Sudoku Class • Edit the file sudoku.py and complete the needed work there • Please follow the class structure and make sure you find all the solutions to the puzzle (not the first one only!)

15. Sudoku Constructor puzzle1 = """ 0 0 3 0 2 0 6 0 0 9 0 0 3 0 5 0 0 1 0 0 1 8 0 6 4 0 0 0 0 8 1 0 2 9 0 0 7 0 0 0 0 0 0 0 8 0 0 6 7 0 8 2 0 0 0 0 2 6 0 9 5 0 0 8 0 0 2 0 3 0 0 9 0 0 5 0 1 0 3 0 0 """ puzzle2 = "005080700 700204005 320000084 060105040 008000500 070803010 450000091 600508007 003010600" puzzle3 = "4.....8.5.3..........7......2.....6.....5.4......1.......6.3.7.5..2.....1.9......" s1 = Sudoku(puzzle1) s2 = Sudoku(puzzle2) s3 = Sudoku(puzzle3) HINT: All we need to do is read 81 digits !We simply skip everything else!

16. Sudoku Constructor (more) # Even this should work ! puzzle4 = """ +-------+-------+-------+ | 0 0 3 | 0 2 0 | 6 0 0 | | 9 0 0 | 3 0 5 | 0 0 1 | | 0 0 1 | 8 0 6 | 4 0 0 | +-------+-------+-------- | 0 0 8 | 1 0 2 | 9 0 0 | | 7 0 0 | 0 0 0 | 0 0 8 | | 0 0 6 | 7 0 8 | 2 0 0 | +-------+-------+-------- | 0 0 2 | 6 0 9 | 5 0 0 | | 8 0 0 | 2 0 3 | 0 0 9 | | 0 0 5 | 0 1 0 | 3 0 0 | +-------+-------+-------+ """ s = Sudoku(puzzle4) # After reading the input, we may do all kinds of methods: s.draw() print s.is_valid() s.solve()

17. Cell Storage puzzle = """ 0 0 3 0 2 0 6 0 0 9 0 0 3 0 5 0 0 1 0 0 1 8 0 6 4 0 0 0 0 8 1 0 2 9 0 0 7 0 0 0 0 0 0 0 8 0 0 6 7 0 8 2 0 0 0 0 2 6 0 9 5 0 0 8 0 0 2 0 3 0 0 9 0 0 5 0 1 0 3 0 0 """ # s consists of 81 intsstored in a dictionary: s.cell: s = Sudoku(puzzle) for i,j in s.cell: print s.cell[i,j] for i,j in s.cell: s.cell[i,j] = 0

18. Sudoku Display • There are two methods for displaying a Sudoku object: • print s • s.draw()Hint: The cells are Rectangle objectswith a label in the middle.The blue blocks can be 9 Rectanglesor a simple draw_grid() – (8 Lines) +-------+-------+-------+ | 4 8 3 | 9 2 1 | 6 5 7 | | 9 6 7 | 3 4 5 | 8 2 1 | | 2 5 1 | 8 7 6 | 4 9 3 | --------+-------+-------+ | 5 4 8 | 1 3 2 | 9 7 6 | | 7 2 9 | 5 6 4 | 1 3 8 | | 1 3 6 | 7 9 8 | 2 4 5 | ----------------+-------+ | 3 7 2 | 6 8 9 | 5 1 4 | | 8 1 4 | 2 5 3 | 7 6 9 | | 6 9 5 | 4 1 7 | 3 8 2 | +-------+-------+-------+

19. row(), col(), block(), diagonals() 1 2 3 4 5 6 7 8 9 +-------+-------+-------+ 1 | 0 0 3 | 0 2 0 | 6 0 0 | 2 | 9 0 0 | 3 0 5 | 0 0 1 | 3 | 0 0 1 | 8 0 6 | 4 0 0 | +-------+-------+-------- 4 | 0 0 8 | 1 0 2 | 9 0 0 | 5 | 7 0 0 | 0 0 0 | 0 0 8 | (puzzle4) 6 | 0 0 6 | 7 0 8 | 2 0 0 | +-------+-------+-------- 7 | 0 0 2 | 6 0 9 | 5 0 0 | 8 | 8 0 0 | 2 0 3 | 0 0 9 | 9 | 0 0 5 | 0 1 0 | 3 0 0 | +-------+-------+-------+ s = Sudoku(puzzle4) s.row(2) => [9, 0, 0, 3, 0, 5, 0, 0, 1] s.row(5) => [7, 0, 0, 0, 0, 0, 0, 0, 8] s.col(2) => [0, 0, 0, 0, 0, 0, 0, 0, 0] s.col(5) => [2, 0, 0, 0, 0, 0, 0, 0, 1] s.block(4,5) => [1, 0, 2, 0, 0, 0, 7, 0, 8] s.diagonals() => ([0, 0, 1, 1, 0, 8, 5, 0, 0], [0, 0, 4, 2, 0, 7, 2, 0, 0])

20. Task 3: Sudoku Solver # This is the hardest part of the project !!! # You will need to design a method: defsolve(self): # self is our Sudoku puzzle instance # All solutions should go into a list self.solutions

21. Sudoku Algorithm: Part 1 • For any cell compute the list of valid values • Example: Valid values of cell (4,1) = 3, 4, 5 • Start by computing what cannot be in the cell • A cell (i,j) is called a singleton if it has exactlyone valid value • Example: Cell (5,6) is a singleton! • What is his single valid value? • A good strategy is to first fill the singleton cells! • After solving singletons • The number of valid values in other cells will be reduced and will make the puzzle easier • After solving all singletons, you will get new singletons … • So you may need to repeat singleton resolution again … 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

22. Sudoku Algorithm: Part 2 • An invalid cell is a cell that cannot be assigned anyvalid value • After resolving all singletons, all remaining cellshavemultiple valid values • The simplest strategy is to select a cell, computehis valid values, and try them all one by one • Once you have selected a valid value and insertedit to the cell, you get a new puzzle with a smallerset of options! • You may use recursion and send the new puzzle and then call yourself recursively !

23. Task 4: Solve a Database of Puzzles • Edit the file: file_solver.py • You will find there the skeleton for the needed function • You have to design a function solve_sudoku_file(file) which accepts a file name of Sudoku puzzles (like top160.txt) and solves all the puzzles in the file • You have to write all the solutions in a new file (like: top160.sol) • See next slide for the format in which the solutions should be written

24. Task 4: Solve a Database of Puzzles top160.sol top160.txt This is the database of 160 difficult puzzlewhich you will find in your Sudoku directory

25. Sudokiller (Bonus) • The project grade weight is 30% but Sudokiller problem can raise it 45% • An algorithm for solving Killer Sudoku puzzles can earn you extra 15% weight to your course grade! (so project grade is 45%) • A Sudokiller puzzle consists of a partition of the board to cages. The number on each cage is the sum of thecells in the cage • You must design the needed datastructures and the algorithmsneeded for solving any sudokiller puzzlein a reasonable time frame (the fasterthebetter your grade is …) • The following puzzle has exactly twosolutions.How fast can you find them?

26. Diagonal Sudokiller • The following three Sudokiller puzzles have also a diagonal solution • You algorithm should also support diagonals too! • Make sure the runtime of your programs does not exceed 10 hours (even for the hardest problem)

27. Sudokiller (puzzle #3)

28. Diagonal Sudokiller (puzzle #4) • This puzzle has two solutions, diagonals included! • You must find them both